Any spell you cast that doesn’t have the type creature will cause prowess to trigger. If a spell has multiple types, and one of those types is creature (such as an artifact creature), casting it won’t cause prowess to trigger. Playing a land also won’t cause prowess to trigger.

9/20/2014

Prowess goes on the stack on top of the spell that caused it to trigger. It will resolve before that spell.

9/20/2014

Once it triggers, prowess isn’t connected to the spell that caused it to trigger. If that spell is countered, prowess will still resolve.